I have read several threads lately about people who want to hit the big prize in a MTT. I too find myself to be one of those players who has found success at the lower limits and dreams of hitting the big prize. Many of us good players will take the occasional shot during an up streak when we have played well, or perhaps when we can win a satellite. But with these big prizes come big stakes, big players, and big variance... So just what are our chances against the big dogs?
One of the problems in calculating variance and chance is a fallacy that exists in our way of thinking. If I play nine 9-person sit and goes, the common thought is that if every player was even, I would win 1 time out of those 9. In reality, though, there is actually only a 66% chance that I will win at least once in those 9 times, with all players being even. See we like to think that with a 1 in 9 chance, 9 tries will give us a probability of 9/9, but we actually have to multiply the chance of not winning (8/9) to the 9th power. This gives you .34 or a 34% chance of not winning. While this isn't profound to some, when you compound it out to multiple entries into MTTs, the numbers can be surprising.
Let's lay out the average “good” player's scenario. For the sake of this discussion, I am going to say that a big cash would be considered $10,000 or more. Here is the plan: I'm going to take the above statistical model and apply it to 10, 100, and 500 entries into 3 of the bigger tournaments on PokerStars. The 3 I have chosen for comparison are the Sunday Million, the Nightly One Hundred Grand, and the nightly $10 rebuy (55k guaranteed).
First we need to set some numbers for these tournaments. I will aim a little high to make sure the odds err on the low side. For the Sunday Million (which varies greatly in terms of participation), I am going to go with an average field of 7000 players. This means a prize pool of 1.4 mill and 8 spots that cash for 10k or more. For the Nightly One Hundred Grand, I am using an average field of 900 players and roughly 3 spots that cash for 10k or more. For the $10 rebuy, I wanted to use the numbers at the end of the first hour, which is generally about 1400 players, and an average amount spent of $51.
Now that we have these stats, I plug them into our formula, and we get some interesting results. Lets start by taking a look at the Nightly One Hundred Grand. This one plays five days a week (with a bigger one on Wednesday; we will leave that out for the sake of this model). I have personally played in 6-8 of these that I can remember, and I cashed once, which was worth twice my buy in, so I have lost money on them personally. The average player like me plays these on occasion.
Let's say you could work it out to play 10 times a year. The odds of hitting a big prize (10k or more), are roughly 3.28% or about 33-1. At first that doesn't sound terrible for the chance of hitting the big one. But applying this same model, you could play this way for 5 years and would still only have a chance of 15% to ever win a $10k+ prize. To make matters worse, there is a 24% chance that you wont finish ITM a single time in 10 tries. Not only that---the $1650 in tournament fees would buy you 7 $215 SNG entries (with some change). The odds of not cashing in at least one of those 7 SNGS is 200-1 (this assumes all players are equal, but you get the idea). 200-1 might sound really high because you an think of times you have lost 7 straight sit and goes, but keep in mind if you played 1500 SNGS a year, this downswing would hit you several times a year.
As you can see, taking 10 shots at the One Hundred Grand is not ideal for variance. Let's step it up though. A lot of good players will use a system where they take a portion of their winnings each day and put it towards satellites for bigger tournaments. So let's say you were a winning player who could afford to play several satellites a week, and on average you won your way into the hundred grand about twice a week, giving you about 100 entries per year. In this case, you would be taking a more serious shot.
How do the numbers play out? The odds of winning our “Big Prize” increase dramatically to 28%. Is the glass half full or half empty? 28% is a lot better than than 3%, but at the same time, there's a 70% chance that you could play for an entire year and not hit the big prize. The chance of winning the whole thing is about 10.5%. Now if you can't cash in 100 tries, you shouldn't be playing poker, so I won't waste time calculating that. Again, though, you are spending $16,200 for a 28% chance to win the big prize, which is the equivalent of 76 ($215) Sit and Go's....
If you played this way for 5 years (500 entries), your odds start to look good, with a 81.16% chance of hitting your big prize (still a 1 in 5 chance you wouldn't hit it in 5 YEARS!!!) and a 42.64% chance of winning a tournament in that 5 years. Could you imagine playing this tournament twice a week for 5 years and not winning once??? It sounds absurd, but the odds are actually against you. Again, this is based on all players being equal; we will discuss the reality that they are not in a bit.
Let's compare these numbers to the other 2 tournaments in our model. The Sunday Million is the behemoth of Poker tournaments. Why drive hours to get to a casino for a $250,000 tournament when I can play in my underwear for 1 mill online?
How do the numbers compare, though? You may be surprised to find out that your chance of winning 10k or more is actually substantially less than in the hundred grand tourneys. For 10 cracks a year, you have about a 1.14% chance of making 10,000$ or more, which is 1/3 of the shot you had in the hundred grand. The odds of winning in 10 tries come out to .14% or 714-1.
So you're spending $2,150 for a 714-1 shot at 200 grand, or about an 88-1 chance of hitting the big prize. If you were to play almost every weekend for 2 years (100 tries), the numbers are still substantially less than in the $100k. You would spend $21,500 and have a 10.81% chance of winning 10k or more once, along with a 1.42% chance of winning $200k. That means if a group of 67 people played every Sunday for 2 years, odds are that one of them would win once.
In evaluating your goals, you have to ask yourself if the shot at 200,000 is worth the decreased chance of our original goal of scoring 10k or more? The Sunday Million costs an extra $53 each time, and our shot is cut in three.
The 3rd tournament we have is the $10 Rebuy tournament. Again, some of these numbers are arbitrary, but we went with an average field of 1,400 people at the end of the first hour, with an average investment of $51(5 buy ins). We also calculated a starting field of about 1,600, meaning 225 will place. Because only one place pays 10 grand or more, this actually gives you the worst chance of hitting a score that big. In 10 tries, there is a .71% chance of winning and grabbing a 10k or more prize. Over 100 tries, this increases to 6.9%, and in 500 tries it's about 30%.
We can't just look at the percentages alone, though. We also have to factor in the cost of the entries. For example, you can play 3 rebuys for the cost of one nightly one hundred grand. We would need to try 3 times as many rebuy tournaments as we do hundred grand entries in order to compare the numbers. With 10 entries, the hundred grand gave you a 3.28% chance of winning 10k or more. When we do 30 entries in the rebuy, your chances are 2.12%. Based on this, we can say that you actually have a better shot for the exact same money in the hundred grand tournament. Not only that, but if you win the 100 grand, you're going to be taking home close to 28k, while the rebuy averages a payout of 12-14k. We already know that the numbers for the Sunday million pale in comparison to the hundred grand tournament, so if our goal is truly to cash for 10k or more, the hundred grand, statistically speaking, would be our best chance and the greatest return on our investment.
As you read this, you need to determine what your ultimate objectives are. Obviously we all want to win money, but I think a lot of people are also looking for respect and the opportunity to be considered an elite player. If this is the case, I still think that cashing a few final tables in the hundred grand is going to be more obtainable and make a bigger splash in the community than getting one lucky hit in the Sunday Million. If you're looking to win 220 grand and somehow magically retire off of it (seems kind of skimpy to me), then by all means go for the gusto.
Now, moving on. All this was based on the premise that all players had an equal chance of winning the tournament. In reality, we know this to not be the case. Aside from variance that can swing in your favor or in your opponent's favor, there simply are players that are better than others, both in general and in relation to the size of the field and/or blind structure. This is good news and bad news depending on who you are. For those of you who are better than the average player in the field, this works to your favor, while for the rest of you, it means the percentages are even worse. While a better player will up the percentages, it is not a drastic amount. At best, I would expect that a quality player could raise their percentages a point or two. While this isn't a drastic statistical change, it can create a dramatic ROI change.
How can you maximize your percentage? There are a couple ways, the first of which is to decrease the cost of your entry with satellites. If you do so, keeping statistics of these satellites is absolutely vital. A good goal to reach for is to win entries for 70% of their value or less. There is a reason for this, and it's simple. Generally speaking, if you can win entries consistently at 70% of their value, then when you finish in the money, you will win at least 2 more entries to that tournament (via satellite).
The reason that is important is that the second way you boost your percentage is by boosting your number of entries. Part of the reason the pros win so many tournaments is that they play so many tournaments. I'm not saying that if you or I played the exact same amount that we would win the same amount, but if you think you'er going to win as many tournaments as JohnnyBax while playing in 1/3 as many as him, you're crazy.
Part of taking a shot to the bigger tourneys and prizes is finding a consistent way to generate winnings. I have my own formula of SNGs, Low level MTTs, and cash games where I can consistently win within my bank roll. With this, I can allot a certain amount to satellites and work accordingly. If this is your goal, you need to find the same. It may mean you have to grind 160 SNGs during the week to win enough money to risk some money on some satellites, so that you can get into the bigger tournaments. This also means that any time you finish in the money and win those 2 buy-ins, you should put them right back into satellites to give yourself additional opportunities. If you can sustain income and satellites, then you have a shot, rather than just a shot in the dark.
Finally, you have to get to a point of comfort where there is no fear of losing and no fear of missing the bubble. Bubble play is one of the most crucial parts of any tournament, and when we play not to lose, we usually end up doing the very thing we tried to avoid. The more you can increase the number of tournaments you play, the less you will be concerned with that specific tournament. If you only play one big MTT a month, chances are you will get real nervous when you start to get close to the money because this is your one shot for the month. If you're playing them every week or a couple times a week, you can play more fearlessly when the crucial points come, thus making the right moves instead of the scared ones.....
I realize that all these numbers can be discouraging and perhaps might discourage you from taking those big chances, and in the end, that might be the best thing for you and your bankroll. If all this hasn't scared you away, the bottom line is that out of the tournaments we've discussed, the Nightly One Hundred Grand is the best bang for your buck. To all of you trying to make that first big score, good luck at the tables.